Combine 3/4 cup sugar, cornstarch, salt, and milk in a heavy saucepan. Cook over medium-high heat, stirring constantly, until thick and bubbly. Continue to boil for one minute. Remove from heat.

In a medium bowl, beat the 3 egg yolks. Gradually stir in 1/4 of the hot mixture into the yolks. Pour yolks back into the remaining hot mixture, stirring constantly. Cook, stirring constantly, for 30 seconds. Remove from heat and add butter, vanilla, and coconut. Pour into the baked pie shell. Cool in the refrigerator.

Preheat the oven to 375 degrees F (190 degrees C).

In a medium glass or metal bowl, beat egg whites until frothy. Slowly add 6 tablespoons sugar while continuing to beat until whites form stiff peaks. Spread meringue over the pie, sealing to the edges and sprinkle with coconut.

Bake in the preheated oven until the meringue is toasted, about 10 to 15 minutes.